{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Further Hypothesis Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──\n",
      "✔ ggplot2 3.3.0     ✔ purrr   0.3.4\n",
      "✔ tibble  3.0.1     ✔ dplyr   0.8.5\n",
      "✔ tidyr   1.1.0     ✔ stringr 1.4.0\n",
      "✔ readr   1.3.1     ✔ forcats 0.4.0\n",
      "── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──\n",
      "✖ dplyr::filter() masks stats::filter()\n",
      "✖ dplyr::lag()    masks stats::lag()\n"
     ]
    }
   ],
   "source": [
    "# Select this cell and type Ctrl-Enter to execute the code below.\n",
    "\n",
    "library(tidyverse)\n",
    "\n",
    "set_plot_dimensions <- function(width_choice, height_choice) {\n",
    "    options(repr.plot.width=width_choice, repr.plot.height=height_choice)\n",
    "}\n",
    "\n",
    "cbPal <- c(\"#E69F00\", \"#56B4E9\", \"#009E73\", \"#F0E442\", \"#CC79A7\", \"#0072B2\", \"#D55E00\")\n",
    "\n",
    "set_plot_dimensions(5, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# You should see \"Attaching packages\" and some ticks by the packages loaded.\n",
    "# The \"Conflicts\" aren't a problem.\n",
    "\n",
    "# Other problems loading the library? Try running this cell.\n",
    "\n",
    "install.packages('tidyverse')\n",
    "\n",
    "library(tidyverse)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 - Comparing means of two groups"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Parsed with column specification:\n",
      "cols(\n",
      "  temperature = col_double(),\n",
      "  luminosity = col_double(),\n",
      "  radius = col_double(),\n",
      "  spectral_class = col_character(),\n",
      "  type = col_double()\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "# Run this cell to load the data.\n",
    "\n",
    "data <- read_csv(\"stars.csv\")\n",
    "\n",
    "type_key <- c('Brown Dwarf', 'Red Dwarf', 'White Dwarf', 'Main Sequence', 'Supergiant','Hypergiant')\n",
    "spectral_classes <- c('O','B','A','F','G','K','M')\n",
    "\n",
    "data$type <- factor(data$type)\n",
    "data$spectral_class <- factor(data$spectral_class, levels=spectral_classes)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For now, let's look at only types 4 and 5 (supergiant and hypergiant). These are of particular interest to your supervisor, Dr Howe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PWHV01NjdTV1QW2zem6YhpY6V8qvkO70kg7SHRfSpQ4RZhIiM8RQAABBBBAAAGX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\nAAJZLfD/AS6oZJJKvFy3AAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data %>%\n",
    "    filter(type %in% c(4,5)) %>%\n",
    "    ggplot(aes(x=log(luminosity), fill=type)) + \n",
    "        scale_fill_manual(values=cbPal[c(5,6)]) +\n",
    "        geom_histogram(alpha=0.5, bins=10) + \n",
    "        guides(fill=\"none\") +\n",
    "        facet_wrap(~ type, ncol=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dr Howe has noticed that supergiants and hypergiants seem to have very similar luminosity distributions. She asks you to check whether they have the same mean."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question: do types 4 and 5 have the same mean luminosity?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The sample means of log(luminosity) are easy to obtain:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Type 4: 12.4848011727945\"\n",
      "[1] \"Type 5: 12.4650579376933\"\n",
      "[1] \"difference: 0.019743235101231\"\n"
     ]
    }
   ],
   "source": [
    "type4 <- \n",
    "    data %>% \n",
    "    filter(type == 4) %>% \n",
    "    pull(luminosity) %>% \n",
    "    log\n",
    "\n",
    "type5 <-\n",
    "    data %>% \n",
    "    filter(type == 5) %>% \n",
    "    pull(luminosity) %>% \n",
    "    log\n",
    "\n",
    "mean4 <- mean(type4)\n",
    "\n",
    "mean5 <- mean(type5)\n",
    "\n",
    "print(paste('Type 4:', mean4))\n",
    "print(paste('Type 5:', mean5))\n",
    "print(paste('difference:', mean4 - mean5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "They are certainly very similar, but is the difference between them statistically significant?\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the histogram, both distributions of log(luminosity) seem approximately symmetrical and with a rough bell-curve, so for now we will assume that they are normally distributed. (We will look later at how to test for normality.)\n",
    "\n",
    "We can therefore choose a **parametric test** for the difference between two means. This means that the test uses a defined probability distribution (e.g. the normal distribution) as a model for the process that generates the data.\n",
    "\n",
    "<br>\n",
    "\n",
    "In general, if the assumptions of a parametric test are satisfied then it will provide more **statistical power** than a non-parametric alternative. Statistical power is defined as the probability that the test *correctly rejects the null hypothesis when it is false*, also known as its *sensitivity* or *true positive rate*.\n",
    "\n",
    "Different parametric test make different **assumptions** about the data, so it is important to think carefully about whether these are satisfied before deciding on a particular test.\n",
    "\n",
    "\n",
    "In this example, a [*t-test*](https://en.wikipedia.org/wiki/Student%27s_t-test) is appropriate:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### t-test for 2 independent groups"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Theory\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When comparing two samples (1 and 2), we will refer to their sizes as $n_1$ and $n_2$, their sample means as $\\bar{x}_1$ and $\\bar{x}_2$ and their sample standard deviations as $s_1$ and $s_2$.\n",
    "\n",
    "Recall that \n",
    "\n",
    "$$\\bar{x} = \\frac{\\sum_{i=1}^n x_i}{n}$$\n",
    "\n",
    "is the *sample mean*\n",
    "\n",
    "and \n",
    "\n",
    "$$s^2 = \\frac{\\sum_{i=1}^n (x_i - \\bar{x})^2}{n-1}$$\n",
    "\n",
    "is the *unbiased sample variance*.\n",
    "\n",
    "<br>\n",
    "\n",
    "For our example, we need a two-tailed test:\n",
    "\n",
    "$H_0$: The two samples come from the same distribution with mean $\\mu = \\mu_1 = \\mu_2$.\n",
    "\n",
    "$H_1$: The samples come from two different distributions, with means $\\mu_1 \\ne \\mu_2$.\n",
    "\n",
    "<br>\n",
    "\n",
    "The test statistic is given by\n",
    "\n",
    "$$t = \\frac{\\bar {x}_1 - \\bar{x}_2}{s_p \\cdot \\sqrt{\\frac{1}{n_1}+\\frac{1}{n_2}}}$$,\n",
    "\n",
    "where \n",
    "\n",
    "$$s_p^2 = \\frac{\\left(n_1-1\\right)s_1^2 + \\left(n_2-1\\right)s_2^2}{n_1 + n_2-2}$$ \n",
    "\n",
    "is an unbiased estimator of the *pooled variance* of the two samples.\n",
    "\n",
    "<br>\n",
    "\n",
    "Under $H_0$, the test statistic $t$ follows a *Student's t-distribution* with $n_1 + n_2 - 2$ degrees of freedom.\n",
    "\n",
    "We use this distribution to calculate a p-value for the observed value of the test statistic, $t$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Assumptions\n",
    "\n",
    "- The means of the two samples follow normal distributions. This is true if the samples themselves are normal, but also true for any other distribution if $n$ is large (by the *central limit theorem*).\n",
    "- The two populations have equal variance.\n",
    "- The two samples are independent.\n",
    "\n",
    "Two-sample t-tests are robust to moderate deviations from these assumptions, but major deviations may produce misleading results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Application\n",
    "\n",
    "$H_0$: $\\mu_{\\text{type4}} = \\mu_{\\text{type5}}$.\n",
    "\n",
    "$H_1$: $\\mu_{\\text{type4}} \\ne \\mu_{\\text{type5}}$.\n",
    "\n",
    "Let's set a significance level $\\alpha=0.05$\n",
    "\n",
    "In R, we just supply the data for each sample and the `t.test` function deals with the rest:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tTwo Sample t-test\n",
       "\n",
       "data:  type4 and type5\n",
       "t = 0.16021, df = 78, p-value = 0.8731\n",
       "alternative hypothesis: true difference in means is not equal to 0\n",
       "95 percent confidence interval:\n",
       " -0.2255986  0.2650851\n",
       "sample estimates:\n",
       "mean of x mean of y \n",
       " 12.48480  12.46506 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t.test(type4, type5, var.equal=TRUE, paired=FALSE, alternative=\"two.sided\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualise this result on the t-distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"degrees of freedom: 78\"\n"
     ]
    },
    {
     "data": {
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lg5rHSKjEAcApqTaY4GW6fpr3HiKGZqt2l71cElqc0gGUMgZwI0sHJW4RQXgTgE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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t_obs <- t.test(type4, type5, var.equal=TRUE, paired=FALSE, alternative=\"two.sided\")$statistic\n",
    "df <- length(type4) + length(type5) - 2\n",
    "print(paste(\"degrees of freedom:\", df))\n",
    "\n",
    "tmin <- -4\n",
    "tmax <- 4\n",
    "x <- seq(tmin,tmax,0.01)\n",
    "plot(x, dt(x,df), xlab=\"t\", ylab=\"pdf\", type=\"l\", col=\"grey\")\n",
    "\n",
    "# the area of the shaded region is the two-tailed p-value\n",
    "lower_tail <- seq(tmin,-t_obs,0.01)\n",
    "upper_tail <- seq(t_obs,tmax,0.01)\n",
    "polygon(c(lower_tail,-t_obs,tmin), c(dt(lower_tail,df),0,0), border=NA, col=\"lightgrey\")\n",
    "polygon(c(upper_tail,tmax,t_obs), c(dt(upper_tail,df),0,0), border=NA, col=\"lightgrey\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The t-test p-value is greater than than $\\alpha$, so we accept the null hypothesis that the means are equal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Other types of t-test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### One-tailed t-test\n",
    "\n",
    "In the example above, we used a *two-tailed test* (because $H_1:\\mu_1 \\ne \\mu_2$ was symmetrical). \n",
    "\n",
    "For a *one-tailed test*, we need to halve the two-sided p-value, e.g. \n",
    "\n",
    "$H_1:\\mu_{\\text{type4}}>\\mu_{\\text{type5}}$ would give us "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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C34Kaq8P2Oujps2bdqz1ag+47xatt12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\ngf8PYf+Ag2EuRUsAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x, dt(x,df), xlab=\"t\", ylab=\"pdf\", type=\"l\", col=\"grey\")\n",
    "\n",
    "# the area of the shaded region is the one-tailed p-value for H1: mu_1 > mu_2\n",
    "upper_tail <- seq(t_obs,tmax,0.01)\n",
    "polygon(c(upper_tail,tmax,t_obs), c(dt(upper_tail,df),0,0), border=NA, col=\"lightgrey\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In R, we can get the upper tail p-value directly by specifying `alternative=\"greater\"` :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"1-tailed p-value: 0.436565642130232\"\n"
     ]
    }
   ],
   "source": [
    "p_upper_tail <- t.test(type4, type5, var.equal=TRUE, paired=FALSE, alternative=\"greater\")$p.value\n",
    "print(paste('1-tailed p-value:', p_upper_tail))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To test the complementary hypothesis (i.e. $H_1:\\mu_1<\\mu_2$), we would need to use `alternative=\"less\"`, which is equivalent to calculating `1 - p_upper_tail`, e.g. \n",
    "\n",
    "$H_1:\\mu_{\\text{type4}}<\\mu_{\\text{type5}}$ would give us"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ECBdAhkPcGaz2G4gHg/8TMipmWI27iK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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x, dt(x,df), xlab=\"t\", ylab=\"pdf\", type=\"l\", col=\"grey\")\n",
    "\n",
    "# the area of the shaded region is the one-tailed p-value for H1: mu_1 < mu_2\n",
    "lower_tail <- seq(tmin,t_obs,0.01)\n",
    "polygon(c(lower_tail,t_obs,-tmin), c(dt(lower_tail,df),0,0), border=NA, col=\"lightgrey\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"complementary p-value: 0.563434357869768\"\n"
     ]
    }
   ],
   "source": [
    "p_complementary <- t.test(type4, type5, var.equal=TRUE, paired=FALSE, alternative=\"less\")$p.value\n",
    "print(paste('complementary p-value:', p_complementary))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "#### Paired two-sample t-test\n",
    "\n",
    "Sometimes we have two samples with paired observations (for example, luminosity of the same set of stars, as measured on two different dates). This situation requires testing whether the *mean of the differences* between pairs is zero, which is called a [*paired two-sample t-test*](https://en.wikipedia.org/wiki/Student%27s_t-test#Dependent_t-test_for_paired_samples).\n",
    "\n",
    "#### Welch's t-test\n",
    "\n",
    "If the sample sizes in the two groups being compared are equal, Student's original t-test is highly robust to the presence of unequal variances. [*Welch's t-test*](https://en.wikipedia.org/wiki/Welch%27s_t-test) is an alternative that is insensitive to equality of the variances, regardless of whether the sample sizes are similar.\n",
    "\n",
    "#### One-sample t-test\n",
    "\n",
    "For cases where we want to compare a sample against a theoretical mean, we can use the [*one-sample t-test*](https://en.wikipedia.org/wiki/Student%27s_t-test#One-sample_t-test)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Alternatives to the t-test\n",
    "\n",
    "#### Mann-Whitney U-test\n",
    "\n",
    "For non-normal samples where $n$ is small, the assumptions of the t-test break down. However, we can use a *non-parametric test* to compare two samples, whatever the shape of their distributions.\n",
    "\n",
    "The [*Mann-Whitney U-test*](https://en.wikipedia.org/wiki/Mann–Whitney_U_test) (aka Wilcoxon rank-sum test) is one such test. The null hypothesis for this test is that a randomly selected value from sample 1 is equally likely to be less than or greater than a randomly selected value from sample 2. If the distributions are sufficiently different, the resulting p-value will be small and we will reject this null hypothesis. Note that the U-test does not compare the sample means directly.\n",
    "\n",
    "\n",
    "#### Wilcoxon signed-rank test\n",
    "\n",
    "The [*Wilcoxon signed-rank test*](https://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test) is is the paired-sample version of the Mann-Whitney U-test.\n",
    "\n",
    "<br>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
